The Apéry numbers, the Almkvist-Zudilin numbers and new series for 1/\pi

• Autores: Heng Huat Chan, Helena A. Verrill
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 16, Nº 2-3, 2009, págs. 405-420
• Idioma: inglés
• DOI: 10.4310/mrl.2009.v16.n3.a3
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• Resumen

  • This paper concerns series for $1/\pi$, such as Sato's series (\ref{eqn:sato}), and the series of H.H. Chan, S.H. Chan and Z.-G. Liu (\ref{eqn:exampleforb_ks}) below.The examples of Sato, Chan, Chan and Liu are related to two index $2$ subgroups of $\Gamma_0(6)_{+}$. These examples motivate us to look at a third subgroup of $\Gamma_0(6)_{+}$. {We give a new method of constructing such series using the theory of modular forms and conclude our work with several new examples.}